Within the context of the electrical power system, “short transmission lines” refer to a specific type of power transmission line that is employed for the purpose of transmitting electricity over “relatively short distances.” In most cases, they are utilized to either connect power producers to the primary electrical grid or to interconnect substations within a specific geographic region. When compared to long transmission lines, short transmission lines are noticeably shorter in comparison in terms of their length.
Because short transmission lines have a low impedance and a low voltage drop, they have a relatively limited effect on the power system as a whole. This is because the line parameters have a comparatively modest effect on the power system. Because of this, we are able to use a lumped parameter model to make the analysis of short transmission lines more straightforward.
When modeling a short transmission line using lumped parameters, the line is modeled as an equivalent circuit with the series impedance (Z) and shunt admittance (Y) coupled in a single location. In the lumped parameter model of a short transmission line, the following is a list of the most important parameters and equations:
Series Impedance (Z):
The series impedance (Z) represents the total impedance of the short transmission line, including both resistance (R) and inductance (L) components. It is typically expressed in ohms.
Z = R + jωL
where:
R = Resistance of the line (ohms)
L = Inductance of the line (henrys)
j = Imaginary unit (√(-1))
ω = Angular frequency of the system (radians per second)
Shunt Admittance (Y):
The shunt admittance (Y) represents the total admittance of the short transmission line, including both conductance (G) and capacitance (C) components. It is typically expressed in siemens (S).
Y = G + jωC
where:
G = Conductance of the line (siemens)
C = Capacitance of the line (farads)
Surge Impedance Loading (SIL):
The surge impedance loading (SIL) of a short transmission line is the maximum power that the line can carry without exceeding a specified voltage limit. It is given by the equation:
SIL = V_base^2 / Z
where: V_base = Base voltage of the transmission line (volts)
Propagation Constant (γ):
The propagation constant (γ) is a complex parameter that accounts for the attenuation and phase shift of the electrical signal as it travels along the transmission line. It is given by:
γ = √(Z * Y)
where: represents complex multiplication
Using phasor notation, which represents voltages and currents as complex values, it is possible to conduct additional research and analysis on the transmission line. We are able to study the behavior of the transmission line under a variety of different operating situations by using the phasor representation. This allows us to determine the voltage drop and current along the line.
In a nutshell, the low impedance and low voltage drop that short transmission lines are known for are their defining characteristics. The study of short transmission lines can be made more straightforward by employing the lumped parameter model, which makes use of the series impedance (Z) and shunt admittance (Y) factors. Because of this simplification, it is now much simpler to research the electrical behavior of short transmission lines and the consequences that these lines have on the power system as a whole.
Transmission lines that have an effective length of less than 80 kilometers (50 miles) or that have a voltage that is lower than 69 kilovolts are considered to be short transmission lines. Because the line charging current is so low, the shunt capacitance can be neglected, in contrast to the situation with medium and long transmission lines.